Final answer:
Without the function's graph or derivative information, we provisionally consider (0.2, -2) as the closest ordered pair to the local minimum, based on its lowest y-value among the choices.
Step-by-step explanation:
To determine which ordered pair is closest to a local minimum of the function f(x), we need to understand how the function behaves near each point. A local minimum occurs where the function changes from decreasing to increasing, which typically corresponds to a point where the derivative (slope) changes from negative to positive.
Looking at the information provided, we are given that at x = 3, the function f(x) has a positive value and a positive slope that is decreasing. The slope decreasing means it is moving towards zero, possibly becoming negative past this point, which suggests a minimum might be near. However, the answer choices provided do not include x = 3, so we have to assess the given points. We need more specific information about the function to determine the exact location of the local minimum, but we can assess the options provided.
Considering the given pairs, (0.2, -2) seems to have the lowest y-value, which might hint at a local minimum, but without the function's graph or derivative, we cannot be certain. Among the choices given and lacking further details on the behavior of f(x), option B is provisionally the closest answer.